Question-165942

Question Number 165942 by Bagus1003 last updated on 10/Feb/22

Commented by naka3546 last updated on 10/Feb/22

Properties of a triangle a + b > c a + c > b b + c > a 1+2 > 3 ?

$$\mathrm{Properties}\:\:\mathrm{of}\:\:\mathrm{a}\:\mathrm{triangle} \\ $$$${a}\:+\:{b}\:>\:{c} \\ $$$${a}\:+\:{c}\:>\:{b} \\ $$$${b}\:+\:{c}\:>\:{a} \\ $$$$ \\ $$$$\mathrm{1}+\mathrm{2}\:>\:\mathrm{3}\:? \\ $$

Commented by ajfour last updated on 10/Feb/22

$${wrong}\:{diagram} \\ $$

Commented by Bagus1003 last updated on 10/Feb/22

$${thats}\:{correct},\:{the}\:{heron}'{s}\:{rule}\:{is}\:{wrong} \\ $$

Commented by MJS_new last updated on 10/Feb/22

no. Heron′s Rule is not wrong. but it only applies to triangles. even in this special case of a degenerated triangle it′s true: the area of a triangle is (L/4) which indeed is zero here.

$$\mathrm{no}.\:\mathrm{Heron}'\mathrm{s}\:\mathrm{Rule}\:\mathrm{is}\:\mathrm{not}\:\mathrm{wrong}.\:\mathrm{but}\:\mathrm{it}\:\mathrm{only} \\ $$$$\mathrm{applies}\:\mathrm{to}\:\mathrm{triangles}.\:\mathrm{even}\:\mathrm{in}\:\mathrm{this}\:\mathrm{special}\:\mathrm{case} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{degenerated}\:\mathrm{triangle}\:\mathrm{it}'\mathrm{s}\:\mathrm{true}:\:\mathrm{the}\:\mathrm{area} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{is}\:\frac{{L}}{\mathrm{4}}\:\mathrm{which}\:\mathrm{indeed}\:\mathrm{is}\:\mathrm{zero}\:\mathrm{here}. \\ $$

Commented by Bagus1003 last updated on 11/Feb/22

$${correct} \\ $$

Answered by alephzero last updated on 11/Feb/22

$${This}\:{is}\:{right}. \\ $$$${Draw}\:{one}\:{side}\:{AB}\:{then}\:{take}\:{a} \\ $$$${compass}\:{and}\:{from}\:{each}\:{point}\:{draw}\: \\ $$$${a}\:{circle}\:{whose}\:{radius}\:{will}\:{be}\:{equal} \\ $$$${to}\:{your}\:{desired}\:{side}.\:{Then} \\ $$$${intersection}\:{of}\:{these}\:{circles}\:{will}\:{be} \\ $$$${point}\:{C}. \\ $$

Commented by alephzero last updated on 11/Feb/22